In
any domain of knowledge, a Smarandache multispace (or S-multispace) with
its multistructure is a
finite or infinite (countable or uncountable) union of many spaces that have
various structures. The spaces may overlap.

The notions of multispace (also spelt multi-space) and
multistructure (also spelt multi-structure) were introduced by Smarandache in
1969 under his idea of hybrid science:

combining different fields into a unifying field,
which is closer to our real life world since we live in a heterogeneous space.

Today, this idea is widely
accepted by the world of sciences.

S-multispace is a qualitative notion, since it is too large and includes both
metric and non-metric spaces.

It is believed that the smarandache multispace with its multistructure is the
best candidate for 21st century Theory of Everything in any domain.
It unifies many knowledge fields.

Applications.

A such multispace can be used for example in physics for the Unified Field
Theory that tries to unite the gravitational, electromagnetic, weak and strong
interactions.

Or in the parallel quantum computing and in the mu-bit theory, in
multi-entangled states or

particles and up to multi-entangles objects.

We also
mention: the algebraic multispaces (multi-groups, multi-rings, multi-vector
spaces, multi-operation systems and multi-manifolds, also multi-voltage graphs,
multi-embedding of a graph in an n-manifold,
etc.), geometric multispaces (combinations of Euclidean and Non-Euclidean
geometries into one space as in Smarandache geometries), theoretical physics,
including the relativity theory, the M-theory and the cosmology, then
multi-space models for p-branes
and cosmology, etc.

- The multispace and multistructure were
first used in the Smarandache geometries (1969),
which are combinations of different geometric spaces such that at least one
geometric axiom behaves differently in each such space.

- In
paradoxism (1980), which
is a vanguard in literature, arts, and science, based on finding common things
to opposite ideas [i.e. combination of contradictory fields].

- In neutrosophy
(1995), which is a generalization of dialectics in philosophy, and takes into
consideration not only an entity <A> and its opposite <antiA> as dialectics
does, but also the neutralities <neutA> in between. Neutrosophy combines all
these three <A>, <antiA>, and <neutA> together. Neutrosophy is a metaphilosophy.

- Then in neutrosophic logic (1995),
neutrosophic set (1995), and neutrosophic probability (1995), which have, behind
the classical values of truth and falsehood, a third component called
indeterminacy (or neutrality, which is neither true nor false, or is both true
and false simultaneously - again a combination of opposites: true and false in
indeterminacy).

In recent decades, Smarandache’s notions of multispace
and multistructure were widely spread and have shown much importance in sciences
around the world. Organized by Prof. Linfan Mao, a professional conference on
multispaces and multistructures, named the First International Conference on
Smarandache Multispace and Multistructure was held in Beijing University of
Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was
announced by American Mathematical Society in advance.

The Smarandache multispace and multistructure are
qualitative notions, but both can be applied to metric and non-metric systems.
There were 46 researchers haven taken part in this conference with 14 papers on
Smarandache multispaces and geometry, birings,
neutrosophy, neutrosophic groups, regular maps and topological graphs with
applications to non-solvable equation systems.

Prof. Yanpei Liu reports on topological graphs

Prof. Linfan Mao reports on non-solvable systems of equations

Prof. Shaofei Du reports on regular maps with developments

Applications of Smarandache multispaces and multistructures underline a
combinatorial mathematical structure and interchangeability with other sciences,
including gravitational fields,
weak and strong interactions, traffic network, etc.

All participants have showed a genuine interest on topics
discussed in this conference and would like to carry these notions forward in
their scientific works.